Metathesis catalysts have been previously described by for example, U.S. Pat. Nos. 5,312,940, 5,342,909, 5,728,917, 5,750,815, 5,710,298, and 5,831,108 and PCT Publications WO 97/20865 and WO 97/29135 which are all incorporated herein by reference. These publications describe well-defined single component ruthenium or osmium catalysts that possess several advantageous properties. For example, these catalysts are tolerant to a variety of functional groups and generally are more active than previously known metathesis catalysts. In an unexpected and surprising result, the inclusion of an imidazolidine ligand in these metal-carbene complexes has been found to dramatically improve the already advantageous properties of these catalysts. For example, the imidazolidine-based catalysts of the present invention exhibit increased activity and selectivity not only in ring closing metathesis (“RCM”) reactions, but also in other metathesis reactions including cross metathesis (“CM”) reactions, reactions of acyclic olefins, and ring opening metathesis polymerization (“ROMP”) reactions.